Reference no: EM13884553

1. Construct categorical derivations for the following tautologies.

a) (P > Q) > ((P> ~Q) > ~P)

b) (P = ~Q)= ~(P = Q)

c) ( P >(P & Q))v( Q > (P&Q))

2. Construct derivations for the following valid arguments.

a) A>~B

~C> B

~A > ~C

  A = C

b)

(P&G)>D

(R&S)>T

P & S

G v R

D v T

c) F > (~G > ~F)
~(H > G) (~H & W)

A > (S & M)

~( A v F)

d) If the cat is ill, either she was fighting or ate too many mice. She was fighting only if she was attacked, and she was attacked only if either the large Siamese or the small Beagle was out. The large Siamese was out only if it was sunny, and the small Beagle was out only if it was warm. It was neither warm nor sunny, but the cat is ill. Therefore, she ate too many mice.